Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 4. Calculation of cyclic trimer content of poly(ethylene terephthalate)

Abstract

The equilibrium concentration of cyclic trimer in poly(ethylene terephthalate) ( pet) melts is calculated by the Jacobson and Stockmayer theory using rotational isomeric state models to describe the conformational statistics of the corresponding linear chains. The Williams and Flory rotational isomeric state model of pet is used for the calculations, together with a model which incorporates structural information made available by a recent study of internal rotation in ethyl formate. This latter model takes into account all the intramolecular interactions within monomeric units by considering interactions that depend on rotations about monads, diads and triads of skeletal bonds. The models define 26244 discrete conformations for the acyclic trimer (CO.C 6H 4.CO.O.CH 2.CH 2.O) 3. The probability that such a chain will intramolecularly cyclize is calculated by computing the total number of conformations that have terminal atoms in close proximity for ring closure, each conformation being accorded a statistical weight based on molecular structural information relating to low molecular weight analogues and on estimates of the steric and electrostatic attractions and repulsions between non-bonded atoms of the chain. The rotational isomeric state models predict the cyclic trimer content of pet melts at 570 K to be 0.1–0.5% by weight (compared with the experimental value of 1·4%) and they give values of the ratio [ 〈r 2〉 0 M ] ∞ of the unperturbed mean-square end-to-end distance of pet to its molecular weight of 0.9–0.6Å 2(g mol.wt.) −1 at 303K (compared with the experimental value of 1·0).